
%!TEX program = xelatex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode

\documentclass[10pt]{article} 

\input{wang_preamble.tex}

\begin{document}

\begin{center}
\includegraphics [width=0.85\textwidth, height=4.1cm]{lixin-pan-new.eps}
\end{center}

\vspace{-0.6cm}

\begin{center}
%{\LARGE\bf 上海立信会计金融学院期终考试卷 --- 试题纸} \hspace{0.3cm} {\Large \underline{ A }卷 }
{\Large\bf \H 上海立信会计金融学院期终考试卷 } \hspace{0.3cm} {\Large \underline{ A }卷 }

\vspace{0.3cm}

{\large \bf \H 2023 $\sim$ 2024 学年 第 二 学期 }

\vspace{0.3cm}

{\large \bf \H \underline{ \emph{2021级数学与应用数学专业} } 《\underline{ \emph{数学写作（全英语）} }》 课程代码：\underline{ 160870213 }  }

\vspace{0.3cm}

{\H（本场考试属\underline{  闭  }卷考试，考试时间共\underline{  90  }分钟，不准使用计算器）共\underline{  4  }页 }
%{\large （本场考试属闭卷考试，考试时间 90 分钟，禁止使用计算器） }

\vspace{0.3cm}

%{\large 本考试卷共 4 页，请在本考试卷上答题。}

%\vspace{-0.3cm}
%\rule[-.3\baselineskip]{\textwidth}{0.2pt}

\vspace{0.4cm}

班级 \underline{\hspace{3.5cm}} 学号 \underline{\hspace{3.5cm}} 姓名 \underline{\hspace{3.5cm}} 

\end{center}

\vspace{-0.2cm}

{\H
\begin{table}[h]
%\caption{Nonlinear Model Results} % title of Table
\centering % used for centering table
\renewcommand{\arraystretch}{1.4}
\begin{tabular}{
|>{\centering\arraybackslash}p{0.9cm}
|>{\centering\arraybackslash}p{0.9cm}|>{\centering\arraybackslash}p{0.9cm}|>{\centering\arraybackslash}p{0.9cm}
|>{\centering\arraybackslash}p{0.9cm}|>{\centering\arraybackslash}p{0.9cm}
|>{\centering\arraybackslash}p{0.9cm}|>{\centering\arraybackslash}p{0.8cm}|>{\centering\arraybackslash}p{1.3cm}|>{\centering\arraybackslash}p{1.2cm}|}
\hline
题号 &一&二&三&四&五&六&总分&合成人签名&审核人签名 \\
%\hline
%应得分&15&15&15&15&15&15&10&100 \\
\hline
得分 $\,\,\,\,\,\,\,\,$ &&&&&&&&& \\
\hline
\end{tabular}
\end{table}
}

%%%%%%%%%%%%%%%%%%%% 试题从这里开始 %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% 试题从这里开始 %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% 试题从这里开始 %%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\vspace{0.3cm}

{\renewcommand{\arraystretch}{2}
\begin{tabular}{|>{\centering\arraybackslash}p{1.5cm}|>{\centering\arraybackslash}p{1cm}|} \hline  & Points \\  \hline\end{tabular}}
%\hspace{0.5cm}{\bf 一、选词填空（每小题 2 分，共 24 分）}
\hspace{0.5cm}{\bf I. Fill in the blanks. (each blank 2 point, total 24 points)}

\vspace{0.2cm}

\begin{enumerate}

\item  
Writing is not simply a task to be done once research or other preparation is completed -- it can be an \underline{\hspace{0.5cm}\hspace{0.5cm}} 
part of the work process. 
%
Writing brings out 
\underline{\hspace{0.5cm}\hspace{0.5cm}}  
in your understanding by forcing you to focus on steps in your thinking that you might otherwise skip. 
%
In this respect, writing is similar to explaining your ideas to a 
\underline{\hspace{0.5cm}\hspace{0.5cm}}  . 
%
Writing down partial research results as your work progresses can reveal 
\underline{\hspace{0.5cm}\hspace{0.5cm}}
and suggest further areas of development. 

\begin{tabular}{p{3cm}p{3cm}p{3cm}p{3cm}}
A1. colleague & A2. gaps & A3. integral & A4. structure  
\end{tabular}

\item  
Writing is difficult. It is often difficult to get started. 
%
One solution, which works for some, is to force yourself to write 
\underline{\hspace{0.5cm}\hspace{0.5cm}}, 
however clumsy it may be, for it is often much more easier to modify something you have written previously than to compose from 
\underline{\hspace{0.5cm}\hspace{0.5cm}}.  
%
The most fundamental tenet of technical writing is to keep your prose 
\underline{\hspace{0.5cm}\hspace{0.5cm}} 
and direct. 
%
Aim for economy of words.
%
Early drafts can usually be reduced in 
\underline{\hspace{0.5cm}\hspace{0.5cm}} 
substantially with consequent improvements in readability. 

\begin{tabular}{p{3cm}p{3cm}p{3cm}p{3cm}}
A5. something & A6. length  & A7. simple  & A8. scratch
\end{tabular}


\item  

Probably the best way to improve your writing skills is to receive, and learn from, constructive 
\underline{\hspace{0.5cm}\hspace{0.5cm}} .  
%
Ask a colleague to read and comment on your writing. 
%
Another reader can often find errors and suggest improvements that you miss because of your familiarity with the work. 
%
It is a 
\underline{\hspace{0.5cm}\hspace{0.5cm}}
to have someone else take the time to comment on your writing.
%
Another way to improve your writing is to 
\underline{\hspace{0.5cm}\hspace{0.5cm}}
as much as you can, always with a 
\underline{\hspace{0.5cm}\hspace{0.5cm}} 
eye. 
%

\begin{tabular}{p{3cm}p{3cm}p{3cm}p{3cm}}
A9. privilege & A10. read  & A11. criticism & A12. critical
\end{tabular}

\end{enumerate}

\vspace{0.2cm}

%{\color{red}Solution. 
%
%}

\vspace{0.2cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage

{\renewcommand{\arraystretch}{2}
\begin{tabular}{|>{\centering\arraybackslash}p{1.5cm}|>{\centering\arraybackslash}p{1cm}|} \hline  & Points \\  \hline\end{tabular}}
%\hspace{0.5cm}{\bf 二、判断对错题（每小题 2 分，共 28 分）}
\hspace{0.5cm}{\bf II. True - False. (each 2 points, total 26 points)}

\vspace{0.2cm}

\begin{enumerate}
\item  In a research paper in linear algebra it would be appropriate to give a lemma stating that the eigenvalues of a symmetric positive definite matrix are positive, as this standard result is so well known; in a textbook for undergraduates, however, it would not be sensible to formalize and prove this result. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item  A pedagogical tactic that is applicable to all forms of technical writing (from teaching to research) is to discuss specific examples after the general case. 
It is tempting, particularly for mathematicians, to adopt the opposite approach, but beginning with examples is often the most effective way to explain. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item  If you have not done so before, it is instructive to study the definitions in a good dictionary. 
They display many of the attributes of a good mathematical definition: they are concise, precise, consistent with other definitions, and easy to understand. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item  In formal writing mathematics is written in complete sentences with proper punctuation, so every piece of mathematics should belong to a sentence. Hence mathematical expressions should always be punctuated. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item  Mathematicians are supposed to like numbers and symbols, but I think many of us prefer words. 
If we had to choose between reading a paper dominated by symbols and one dominated by words then, all other things being equal, most of us would choose the wordy paper, because we would expect it to be easier to understand. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item  An equation is not displayed when it needs to be numbered, when it would be hard to read if placed in-line, or when it merits special attention, perhaps because it contains the first occurrence of an important variable. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item  Parallelism is the expression of parallel ideas in parallel grammatical form, including in mathematical expressions. 
Parallelism should be used, where appropriate, to aid readability and understanding. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}
 
\item  By convention, variables are set in roman font and standard mathematical functions such as sin, cos, arctan, max, gcd, trace, and lim are set in italic font, as are multiple-letter variable names. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item   When you reference an earlier equation it helps the reader if you add a word or phrase describing the nature of that equation. 
The aim is to save the reader the trouble of turning back to look at the earlier equation. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item
The normal practice when introducing a nonstandard abbreviation or acronym is to spell out the word or phrase in full on its first occurrence and place the abbreviation immediately after it in parentheses. 
Thereafter the abbreviation is used. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item  
Prefer the passive voice (``Y was done by X'') to the active voice (``X did Y''). 
The passive voice adds life and movement to writing, whereas too much of the passive voice weakens the communication between writer and reader. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item  English is one of the most synonym-rich languages, thanks to the words it has adopted from other languages, and each member of a set of synonyms can have a different tone and shade of meaning. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}

\item  A standard device for making text more appealing is to break it into small paragraphs, as is done in newspapers. 
To communicate complex ideas in technical writing, long paragraphs are certainly helpful. 
Ideally, each paragraph contains a main idea or thought that separates it from its neighbors. 
Short paragraphs tend to give a page a heavy look that can be a visual deterrent to the potential reader. 
\dotfill \underline{(\hspace{0.3cm} \hspace{0.3cm})}


\end{enumerate}

\vspace{0.2cm}

%{\color{red}Solution. 
%
%}

\vspace{0.2cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage

{\renewcommand{\arraystretch}{2}
\begin{tabular}{|>{\centering\arraybackslash}p{1.5cm}|>{\centering\arraybackslash}p{1cm}|} \hline  & Points \\  \hline\end{tabular}}
%\hspace{0.5cm}{\bf 三、多项选择题（每小题 2 分，共 20 分）}
\hspace{0.5cm}{\bf III. Choose the better way of writing. (each 2 points, total 20 points)}

\vspace{0.2cm}

\begin{enumerate}

\item  
\begin{enumerate}
\item  The result is obtained by using Lemma 2.1, Theorems 2.5 and 3.1.
\item  The result is obtained by using Lemma 2.1 and Theorems 2.5 and 3.1. %Better
\end{enumerate}

\item  
\begin{enumerate}
\item  These bounds are sharp and scale independent but expensive to compute. %Better
\item  These bounds are sharp, scale independent, but expensive to compute.
\end{enumerate}

\item  
\begin{enumerate}
\item  If $x> 1$, $f(x) < 0$.
\item  If $x> 1$ then $f(x) < 0$. %Better
\end{enumerate}

\item  
\begin{enumerate}
\item  Since $p^{-1} + q^{-1} = 1$, the norms $\lVert \cdot \rVert_p$ and $\lVert \cdot \rVert_q$ are dual. %Better
\item  Since $p^{-1} + q^{-1} = 1$, $\lVert \cdot \rVert_p$ and $\lVert \cdot \rVert_q$ are dual norms. 
\end{enumerate}

\item  
\begin{enumerate}
\item  It suffices to show that $\lVert H \rVert_p = n^{1/p}, (1 \le p \le 2)$.
\item  It suffices to show that $\lVert H \rVert_p = n^{1/p}$ for $1 \le p \le 2$. %Better
\end{enumerate}

\item  
\begin{enumerate}
\item  For $n = r$, inequality (2.2) holds with $\delta_r = 0$. %Better
\item  For $n = r$, (2.2) holds with $\delta_r = 0$.
\end{enumerate}

\item  
\begin{enumerate}
\item  Let $A = QTQ^*$ be a Schur decomposition.  %Better
\item  Let the Schur decomposition of $A$ be $QTQ^*$.
\end{enumerate}

\item  
\begin{enumerate}
\item  Under what conditions does the iteration converge to the solution of $f(x) = 0$?
\item  Under what conditions does the iteration converge to a solution of $f(x) = 0$? %Better
\end{enumerate}

\item  
\begin{enumerate}
\item  A numerical example is now given to illustrate the above result. 
\item  We give a numerical example to illustrate this result.  %Better
\end{enumerate}

\item  
\begin{enumerate}
\item  Beltrami derived the singular value decomposition for square, nonsingular matrices.  %Better
\item  Beltrami essentially derived the singular value decomposition. 
\end{enumerate}

\end{enumerate}

\vspace{0.2cm}



\vspace{0.2cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\vspace{0.2cm}

{\renewcommand{\arraystretch}{2}
\begin{tabular}{|>{\centering\arraybackslash}p{1.5cm}|>{\centering\arraybackslash}p{1cm}|} \hline  & Points \\  \hline\end{tabular}}
%\hspace{0.5cm}{\bf 四、改写题（每小题 4 分，共 20 分）}
\hspace{0.5cm}{\bf IV. Proofreading. (each 2 points, total 10 points)  }

\vspace{0.2cm}

\begin{enumerate}

\item  
Substituting (3) into (7), the integral becomes $\pi^2/9$.

\underline{Correction.}

\vspace{0.4cm}


\item  
If $y_1, y_2, \cdots, y_n$ are all $\neq 1$ then $g(y_1, y_2, \cdots y_n) >0$.

\underline{Correction.}

\vspace{0.4cm}


\item  
It is easy to see that $f(x, y) > 0$ for $x > y$. 

\underline{Correction.}

\vspace{0.4cm}

\item  
$A$ is an ill-conditioned matrix. 

\underline{Correction.}

\vspace{0.4cm}

\item  
It is not unreasonable to assume uniqueness of $x^*$. 

\underline{Correction.}

\vspace{0.4cm}


\end{enumerate}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage

{\renewcommand{\arraystretch}{2}
\begin{tabular}{|>{\centering\arraybackslash}p{1.5cm}|>{\centering\arraybackslash}p{1cm}|} \hline  & Points \\  \hline\end{tabular}}
%\hspace{0.5cm}{\bf 五、短文写作题（共 10 分）}
\hspace{0.5cm}{\bf V. Passage. (total 10 points)}

\vspace{0.2cm}

Solve the following problem. Make sure that you use complete sentences.

\vspace{0.2cm}

\underline{Problem.}
Verify the rule $\det(AB)=\det(A)\det(B)$ for the matrices 
$$A=\begin{bmatrix}2&0 \\ 2&4\end{bmatrix} \,\,\mathrm{and}\,\, B=\begin{bmatrix}2&2\\ 2&4\end{bmatrix}. $$

\vspace{0.3cm}

\underline{Solution.}



\vspace{4.5cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace{0.2cm}

{\renewcommand{\arraystretch}{2}
\begin{tabular}{|>{\centering\arraybackslash}p{1.5cm}|>{\centering\arraybackslash}p{1cm}|} \hline  & Points \\  \hline\end{tabular}}
%\hspace{0.5cm}{\bf 六、英语写作风格（共 10 分）}
\hspace{0.5cm}{\bf VI. Elements of Style. (each 2 points, total 10 points)}

\vspace{0.2cm}

Explain the following elementary principles of composition. 

\vspace{0.2cm}

\begin{enumerate}
\item  Make the paragraph the unit of composition, one paragraph to each topic. 

\underline{Explain.} 

\vspace{1.3cm}

\item  As a rule, begin each paragraph with a topic sentence. 

\underline{Explain.} 

\vspace{1.3cm}

\item  Use the active voice. The active voice is usually more direct and vigorous than the passive. 

\underline{Explain.} 

\vspace{1.3cm}

\item  Put statements in positive form.

\underline{Explain.} 

\vspace{1.3cm}

\item  Avoid a succession of loose sentences.

\underline{Explain.} 

\vspace{1.3cm}


\end{enumerate}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}





